We introduce and validate a delensing framework for the Simons Observatory
(SO), which will be used to improve constraints on inflationary gravitational
waves (IGWs) by reducing the lensing noise in measurements of the $B$-modes in
CMB polarization. SO will initially observe CMB by using three small aperture
telescopes and one large-aperture telescope. While polarization maps from
small-aperture telescopes will be used to constrain IGWs, the internal CMB
lensing maps used to delens will be reconstructed from data from the
large-aperture telescope. Since lensing maps obtained from the SO data will be
noise-dominated on sub-degree scales, the SO lensing framework constructs a
template for lensing-induced $B$-modes by combining internal CMB lensing maps
with maps of the cosmic infrared background from Planck as well as galaxy
density maps from the LSST survey. We construct a likelihood for constraining
the tensor-to-scalar ratio $r$ that contains auto- and cross-spectra between
observed $B$-modes and lensing $B$-mode template. We test our delensing
analysis pipeline on map-based simulations containing survey non-idealities,
but that, for this initial exploration, do not include contamination from
Galactic and extragalactic foregrounds. We find that the SO survey masking and
inhomogeneous and atmospheric noise have very little impact on the delensing
performance, and the $r$ constraint becomes $sigma(r)approx 0.0015$ which is
close to that obtained from the idealized forecasts in the absence of the
Galactic foreground and is nearly a factor of two tighter than without
delensing. We also find that uncertainties in the external large-scale
structure tracers used in our multi-tracer delensing pipeline lead to bias much
smaller than the $1,sigma$ statistical uncertainties.
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